Paper EL+AS+BI+EM+SS-FrM6
A Classical Model for Depolarization through Incoherent Superposition of Dipoles Driven by Evanescent Fields

Friday, November 14, 2014, 10:00 am, Room 304

A finite spectral resolution and/or an imperfectly collimated beam /and or an (areal) extended light source / and or an (areal) extended detector and/ or a sample with a varying thickness can produce depolarization effects. However, despite these experimental findings, there are to our knowledge no physical models published which trace the origin of depolarization back to the atomic properties. Therefore, we explain depolarization by the following steps:

1) A mathematical model for cross- polarization: In structured samples the Fresnel reflectances are not correct any more, they rely on homogheneity (i.e. an arbitrary shift of the sample along any surface direction). Mathematicians are aware of this and the numerical tools developed by them, e.g. finite element methods (FEM) or rigorous coupled wave analysis (RCWA), take these effects into account, when matching boundary conditions. Mathematically the Jones matrix then possesses nondiagonal elements. This cross polarization signifies the presence of a totally polarized photon state, but takes into account that p- polarized incoming light creates s- polarized outgoing and vice versa.

2) Cross- polarization then has to take into account radiating dipoles, whose radiation create the scattered cross (and later, after incoherent superposition, partially de-) polarized field. In any structured sample there are inner boundaries present and it is straightforward to show that the usual boundary conditions on the continuity of the tangential electric field and the normal of the displacement field yield inherent contradictions at these inner boundaries. In order to fulfill the boundary conditions, close to the inner boundaries evanescent fields must be present, which drive the atomic dipoles in other spatial directions than the incoming field.

3) Depolarization: The end point of the field of unpolarized light may be assumed to move quite irregularly, and the light shows no preferential directional properties when resolved in arbitrary orthogonal directions normal to the direction of propagation. Depolarization is mathematically described by the correlation which exists between these two orthogonal directions. Furthermore the extension of the light source, the extension of the detector and the extension of the illuminated sample area (especially its depth!) are reducing the value above. The measured intensity at the detector is obtained by the incoherent superposition of the single waves. The mathematical formulation is given by the Cittert- Zernike theorem (M. Born & E. Wolf, Principles of Optics, chapter X.9).